Comparison of quiver varieties, loop Grassmannians and nilpotent cones in type A


Abstract in English

In type A we find equivalences of geometries arising in three settings: Nakajimas (``framed) quiver varieties, conjugacy classes of matrices and loop Grassmannians. These are now all given by explicit formulas. As an application we provide a geometric version of symmetric and skew $(GL(m), GL(n))$ dualities.

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